Jack Dorsey, of Twitter, is now making big money at Square—and is out to prove that he’s more than a lucky man.

Jack Dorsey, the tech entrepreneur, takes the No. 1 bus to work, and he likes to catch the 7:06. It carries him nearly from one side of San Francisco to the other—down California Street almost to Market. A ride costs two dollars, but Dorsey has a monthly pass, so the actual price, he told me on a recent commute, is closer to a dollar seventy-five. “If you buy it in bulk, it saves you a little bit of money,” he explained. As we got on, he added, “I love the bus. It’s consistent, and it runs every few minutes. But it’s also express. If I took another bus, it’d be stopping.” The offices of Square, his mobile payment-processing service, just moved. He used to follow his bus ride with a pleasant twenty-minute walk down Mission to the San Francisco Chronicle Building, where Square rented office space; now his commute ends with a short ride on a Muni train to Square’s new headquarters, which have a panoramic view of the city. When we got to the Muni stop, Dorsey, who is thirty-six, pointed it out with the excitement of a six-year-old.

Dorsey loves cities and the way movement within them can be charted and broken down into millions of parts. A city is a system that is at once flexible and stable, searchable and random. He expressed a similar interest in ant communities and aspen trees. “I really like any colony-based structure, where you have a strong dependence on a network,” he said. “Aspen trees grow in groups. If one of them dies, they all suffer. I think humans have the same thing, though it’s not as much on the surface.” He likes to draw ferns. (In his twenties, he studied botanical illustration.) “They’re a single structure that tends to repeat itself,” he said. “They’re fractal.” Exotic as these enthusiasms are, they seem suspiciously apt for the creator of Twitter, a service defined by its “strong dependence on a network.” As a thinker, Dorsey seems at once earnest and improbably coherent.

Dorsey, who is six feet tall and narrow of frame, sat in the back of the bus. He likes to observe other commuters and silently perform market research. Who is on a smartphone or a tablet, and who is just staring off into space? “I saw the rise of Instagram here,” he said. “I saw the rise of Vine and Snapchat, and how many more people were using Facebook versus Twitter, and it’s amazing. Like, look—anyone reading magazines, newspapers, books?” The bus ride also allows him to check his account on Twitter, which he helped found, in 2006. His Twitter handle, @Jack, was the twelfth account in the system, but, because the first eleven were tests, he is actually the first of the service’s half-billion users.

Bridges are another of his passions. He recently bought a modern house with a view of the Golden Gate, for ten million dollars. He commemorated the purchase with a lofty tweet: “ ‘I need the sea because it teaches me.’—Pablo Neruda.” Dorsey says that he is less interested in individual poems than in “getting something down to its essence, the economy of words.” He is a techno aesthete in the manner of Steve Jobs: Dorsey, too, is a college dropout, a taker of long walks, and a guy whose father liked to tinker. And, just as Jobs, with his Issey Miyake turtlenecks, tried to embody Apple’s sleek functionalism, Dorsey’s tastes are self-consciously in synch with the design of Twitter. “Constraint inspires creativity” is one of his credos. Formerly a vegan—too much beta-carotene turned his skin orange—he is now on the Paleo diet, which forbids refined sugar and grains. When he was a teen-ager, Dorsey told me, he read a book about tea ceremonies and was impressed by the Japanese precept of wabi-sabi, which holds that the greatest beauty comes from organization with a dash of disorder. “The monks rake up leaves, then they sprinkle a few leaves back,” he explained.

On the bus, Dorsey opened an iPad Mini. Everything he reads, works on, or thinks about resides either in the tablet’s memory or in the Cloud. Twitter—inspired by the text message—is all about immediacy and mobility, and so is Dorsey. He carries no briefcase or folder, and has no desk at work. In my visits with him, in the course of several months, I never saw him handle a piece of paper. When people give him books, he says, he gives them away, then downloads the e-book, which he usually deletes from his iPad after he’s finished. He once hoped to have a big library, but he prefers this: what good is information if you can’t have access to it whenever you like? He owns a Leica, but mostly takes pictures with the iPhone. “The best camera is the one you carry with you,” he says. He gets about a hundred e-mails a day and culls them nightly. “I keep my address pretty private,” he says. “That keeps it down, because it’s such a burden.” This obsession with streamlining helped Dorsey create Square, whose first product was a credit-card reader that attaches to mobile devices through a headphone jack. Square technology, he hopes, will one day kill the cash register, simplifying commerce the way Twitter simplifies online communication.

As our bus bounced along, news helicopters were circling over City Hall. The previous day, the Supreme Court had voted to uphold gay marriage—a particularly big deal in San Francisco. Dorsey, who is a liberal, later tweeted, “Accept people everywhere.” But he was even more excited about Wendy Davis, a Texas state senator who had just held an eleven-hour filibuster in Austin, in an attempt to block new abortion restrictions. Her protest caught the mainstream press by surprise. The Texas fight was a local eruption of an issue of national interest, which is where Twitter’s advantage as an information-spreading organization kicks in. While Davis spoke, more than half a million supporters sent out tweets with the hashtag #StandWithWendy. Tweeters read one another’s tweets and retweeted them, making Davis’s pink sneakers famous in the process. They also disseminated a picture indicating that Texas Republicans had not brought the bill to a vote until after a midnight deadline. Dorsey, who has 2.4 million followers, retweeted some of the images. Cumulatively, Twitter established a powerful account of the filibuster; it lacked the coherence of a good newspaper analysis, but it was more visceral. One piece of the mosaic was provided by a tweet from President Barack Obama’s account: “Something special is happening in Austin tonight.”

Late last year, Twitter, at Dorsey’s urging, bought Vine, which allows the user to attach a short video—six seconds or less—to Twitter posts. During the filibuster, thousands of users did so. “That was the first time I really saw Vine in action at an event like that,” Dorsey said. He then said something that sounded like a sponsored tweet: “Twitter has this unique ability to bring you closer to whatever you care about the most.” He makes such sculpted observations repeatedly. At another point, he told me, “Twitter is about moving words. Square is about moving money.”

The tweets about Davis’s speech were overwhelmingly supportive—the service’s users often champion liberal causes. Dorsey added a dollop of self-congratulation to the coverage: “I am so proud of all the people using Twitter and Vine.” Nevertheless, he insists that Twitter is neither liberal nor conservative; it’s a public utility, like water or electricity. “I like technology that is unbiased,” he says. His goal in life, however, is a frankly progressive one: by making information freer, he hopes to make the world fairer, kinder, and nicer. (Twitter is blocked in China, Syria, and Iran.)

The endless expansion of information on the Internet has created a countervailing appetite for compressed and concise media. But when Twitter first attracted wide attention, in 2007, many commentators took the word limit on posts—a hundred and forty characters—as confirmation of its banality. One early appraiser made a crack that has been tweeted thousands of times since: “This is like the Seinfeld of the Internet—a website about nothing.” Dorsey has sent his share of inessential tweets. “A passenger mirror. Thoughtful addition to a taxi,” he recently tweeted, with a Vine of the same. But when Twitter was created Dorsey knew that he was introducing a mutable medium, even if he wasn’t sure what forms it could take. It turned out that Twitter could accommodate serious subjects: word of the death of Osama bin Laden broke on Twitter, and during the Arab Spring users saw revolutions unfold in real time. The service has become the preferred way to exchange links to long articles. Even on the level of language, Twitter’s constraint has inspired creativity, forging original forms such as the hashtag, which has become so popular that people often insert jokey ones into their e-mails.

Twitter’s critics dismiss it as yet another online opportunity for narcissism, and Dorsey’s feed could be seen as evidence of this. He occasionally turns philosophical: a few weeks ago, he asked his followers, “What is the biggest issue facing civilization today?” And after Iran’s new leader, Hassan Rouhani, joined Twitter, Dorsey greeted him and then asked a tough question: “Good evening, President. Are citizens of Iran able to read your tweets?” But he’s partial to tweeting selfies. This past year, Dorsey, who is scruffily handsome, posted so many Vines of himself that the tech press began to object. The Web site Valleywag complained that Dorsey was “starting to straight up frighten us. Is staring blankly into a camera every day the best way to get people to use your app?” More recently, Dorsey has been posting Vines that offer a glimpse of his girlfriend, Kate Greer, who is a social-media entrepreneur. The videos show them having fun in wonderful places like Big Sur and Marfa, Texas. Dorsey knows that some people find such tweets to be preening, but he told me that he’s leading by example when his feed playfully reveals that, say, he prefers to get his hair cut at an old-time barbershop. “We put a lot of public figures up on a pedestal, and that’s a mistake,” he says. “Some of those small details of life—here’s a beautiful sunset—make everything feel a lot smaller, and more human.” Perhaps, but in Dorsey’s case the small details he presents to the world are relentlessly glamorous. Those grainy, jumpy Vines transform Dorsey and Greer into an alluring couple from a New Wave film. Their effect is to make Dorsey seem larger, and maybe even a bit less human.

Dorsey now spends most of his time working at Square, which launched in 2010. Soon after Twitter was founded, Dorsey became its C.E.O., but in 2008 he lost that position after complaints piled up that the former coder had become a distracted manager. In 2011, he returned to Twitter, in a lesser executive position, and began dividing his time evenly between Square and Twitter. But the pace was exhausting, and he alienated some Twitter employees. He now comes in to the Twitter offices only once a week. No one at Twitter reports to him directly anymore, and he is left to think about how to make Twitter a better product. He also attends board meetings.

One Tuesday in June, I found him in his office at Twitter with his iPad Mini, looking a bit unmoored. “This is, like, my space,” he said. An extra-large soccer jersey with his name on it hung on the wall. “It’s the wrong size. It was a gift.” Recently, Dorsey has focussed on tightening Twitter’s control over the look and functionality of its service across platforms. Independent developers had created superior interfaces for reading and organizing tweets, meaning that Twitter was no longer defining the user experience. The company, controversially, has begun revoking the access of these developers and supplanting their creations with in-house products. Dorsey defends this shift in the name of simplicity. “When people go to the App Store and type in ‘Twitter,’ they don’t expect a million different apps,” he said. “They expect to find one—from the company.” Vine was a key purchase, a counterpunch to Facebook’s acquisition of Instagram. Dick Costolo, the C.E.O. of Twitter, recalls how Dorsey pitched Vine to him: “ ‘I think you need to talk to these guys. It’s the perfect way of thinking about constrained media as a complement to constrained text.’ ”

Dorsey had reservations for dinner that evening at Zuni, an organic café on Market Street. He has a weekly restaurant schedule: “Zuni on Tuesday, Aziza on Monday, 54 Mint on Wednesday. Thursday, Tiburon. Friday, I don’t go anywhere.” This habit, naturally, had a theory behind it. “There’s an approach of going really deep or going really broad. I’m always looking for the one thing for me, rather than tasting everything I can. If you have a table in a consistent space, you can actually notice more things within it.”

Dorsey’s emulation of Steve Jobs diverges in at least one key respect: whereas Jobs overwhelmed those around him, Dorsey is the kind of leader who never feels the obligation to fill a silence. Before he was famous, this allowed him to fade into the background. “I’m perfectly happy being by myself, walking and thinking, and going to movies by myself,” he says. “A lot of people are not comfortable doing things completely alone, but I am.” Now that he is powerful, people monitor him closely. Robert Andersen, one of Square’s creative directors and a friend of Dorsey’s, told me, “If he says something at a meeting, you better listen—he would not have spoken if he didn’t have something important to say.”

The next day, at Square, I watched him meet with half a dozen designers. They discussed the look of Square’s Web site. What was the optimal color palette? Should photographs have borders, or extend to the edge of the browser? The meeting was held standing up. Dorsey plants his feet evenly and holds himself erect, his body still; although he has inviting blue eyes, he tends to look away from people. At first, he seemed to be satisfied with the demos, but then he issued a cautionary decree, so softly that I had to lean in to hear it: “Apple is moving in this direction. . . . We can’t be a version of what they’re doing, and right now we are.” He added, “Get away from white as much as you can.” Some of the designers protested, but soon gave way: Square is Dorsey’s company. It is his do-over, after a messy experience with Twitter. “I want us to have a unique voice,” he explained to me later. Square’s credit-card reader is used by many artisanal businesses. “Our niche is countertops and farm stands.” Square’s Web site needed to emphasize a cozy sense of community, rather than look coldly corporate.

Dorsey’s interest in aesthetics runs deep but feels learned, like the voice of a newly adolescent boy. When I first met him at Twitter, he was wearing jeans, a Dior shirt with a reverse collar, and handcrafted cowboy boots. He once tweeted, “I love espadrilles. And this glass of wine. And the word ‘asperity.’ ”

Dorsey isn’t grand: you can tease him about his fancy boots or the fact that he’s making a lot of money by “democratizing” payments. His humor is often self-deprecating. One day at Square, I noticed a news item on his Twitter feed, which suggested that Square Market, a new online bazaar of offerings by Square merchants, might give Amazon a run for its money. “Oh, Jeff Bezos is trembling,” he said. “He can’t think of anything else.”

According to Forbes, Dorsey is America’s sixth-youngest billionaire. Seven years ago, he was in debt. He seems somewhat discomfited by this turn: he likes money but dislikes himself for liking it. At one point, he commented, “One of my ex-girlfriends said to me, ‘Money is round. It’s made to roll.’ I definitely took that in.” He quickly added, “It really weighs on me. I definitely feel the most fundamental issue is economic equality.” At another point, he told me, “My life hasn’t changed much. I still draw. I still use my journal.” Biz Stone, a co-founder of Twitter and a friend of Dorsey’s, says that Dorsey “still has this way about him that is, like, ‘The ginkgo leaf is the perfect leaf. That’s why it’s the only leaf I draw.’ And now he’s able to say, like, ‘The BMW is the only car I drive, because it’s the best automotive engineering on the planet,’ or whatever. It was a ginkgo leaf before, and now it’s a Prada suit.” Like Dorsey, Stone talks in aphorisms, and one of them is this: “Money makes people just more of what they were before.”

Enormous wealth rubs against Dorsey’s impulse to simplify. He pointed out that, before he moved into his big new house on the Bay, he lived happily in a small studio. Square is an attempt to pare down the process of buying something. One of the company’s offerings, Square Wallet, allows shoppers to use their smartphones to make cashless purchases. The phone beams information to the merchant’s iPad, which calls up a picture and an account on file. “You pay with your name,” Dorsey says. To show how this worked, he took me to a favorite San Francisco coffee shop, Blue Bottle. “I’m Jack,” he said to the barista, thrilled, and took his espresso without reaching for his wallet.__

Jack Dorsey was born in 1976, and grew up in a working-class family in St. Louis. His father, Tim, worked in the service department of a company that manufactured mass spectrometers. His mother, Marcia, was a homemaker. When he was a teen-ager, she owned a café where he occasionally worked as a barista. He recalls, “The first time I made a cappuccino, the milk was spilling everywhere and I didn’t put enough coffee in, and the person buying it said it was the best cappuccino ever.” Beat. “St. Louis didn’t have a lot of cafés back then.”

As a child, Dorsey was quiet and self-sufficient. His mother remembers him, as a three-year-old, spending an entire day in a shirt and a tie, and staying “neat as a pin.” He learned to draw from his mother, and enjoyed making portraits. “I would do a lot of faces, mainly with an H.B. pencil. I was definitely an observer.” He made pointillist drawings. (His parents still have one that he made, later, of Kurt Cobain.) When he was young, he was afflicted by a speech impediment. “When you’re doing something and you’re doing it wrong, you usually either stop it or try to fix it,” he says. “I did a bit of both.” Dorsey developed an aversion to casual communication, and at school he joined the debate team and the speech club. Tim Dorsey took him to a Cardinals football game when he was eight or nine. “He brought a book,” Tim recalls, adding, “We don’t know where he came from!” Tim and Marcia were taken aback when Jack, the oldest of three boys, insisted on the smallest bedroom. “He was always a minimalist,” his mother told me.

One of his father’s favorite pastimes was to drive down to the Mississippi and listen to CB-radio calls from barges floating by. (His father now tweets the river news and posts Vines of the boats.) Dorsey borrowed the radio, added a police scanner, and installed them in his room. The barges didn’t hold his interest: “It’s the most boring thing in the world.” But he was thrilled by the police scanner, and still remembers its staccato transmissions. “They were reporting constantly, and they’re reporting three things usually. No. 1, where they are. No. 2, where they’re going. And, No. 3, what they’re doing. So, for an ambulance in St. Louis: ‘I’m at Fifth and Broadway, I’m going to St. John’s Mercy, patient in cardiac arrest.’ ”

Dorsey wanted to chart these movements. In 1984, when he was eight, his father bought him an I.B.M. PC Jr.; three years later, he was given a Macintosh. St. Louis was a technologically advanced city then, home to McDonnell Douglas and Southwestern Bell. Phrack, an online magazine for hackers, was based there. Washington University let locals use its computer network, and Dorsey tapped in so that he could gain access to the Internet. He particularly loved Internet Relay Chat, which allowed him to watch programmers trading code. “It was like a big Internet CB radio,” he says. He remembers using it to teach himself to code in C, and he wrote a program that graphically simulated the movements of the vehicles on the police scanner. “It’s a rush,” he says. “You forget to sleep. You forget to eat. I just felt so great, because, Oh, I can actually build something that enables me to see the city.” This was the start, he said, of his interest in converting “to the virtual what was happening in the physical.” But he soon realized that a key element was absent. “I could see ambulances, I could see black cars, but I was missing the individuals.”

Dorsey attended Bishop DuBourg, a Catholic high school in south St. Louis. In 2009, his friend Tim Brouk told the Post-Dispatch that Dorsey was one of “the more popular unpopular guys in our class.” Dorsey ate lunch every day at the same table, with Brouk and another friend, Charlie Kelly, and was one of the hosts of a closed-circuit TV show, covering the “status of everything that was happening at the school.” Kelly remains mystified how his reserved friend knew so much. “I’m a great listener, I guess,” Dorsey says. “I like to know what’s going on.” He had a girlfriend and cool music in his car—Brouk remembers listening with him to the ska band Operation Ivy—and he drove his friends to local clubs. (They didn’t drink, though; Dorsey didn’t touch alcohol until he was twenty-two.) Dorsey likes to point out a parallel between the I.R.C. channels he read and the bands he watched: “They would go out onstage, and then everyone would throw things at them, and every week they would get better and better and better. So it’s like performing in public and learning in public and making all your mistakes in public, which is exactly what you do with open-source code.”

Dorsey ran a football pool, and handed out the forms in neat plastic bags that his father had brought home from work. He closed the bags with a hot sealer. “On Monday, I printed out these sheets for the games ahead,” he remembers. “And on Sunday night I would just tally everything up. I don’t know why I loved doing it, but it was a little system that I could control and play with.”

In 1995, Dorsey enrolled in the University of Missouri at Rolla, where he majored in computer science and math. But the practical had always interested him more than the theoretical, the sociological more than the technological. “I wanted to build more instead of learn more,” he remembers. He still worked on the routing-map project. One day during his junior year, he was surfing the Internet and came across the Web site of Dispatch Management Services, which managed bicycle messengers in New York. He hacked into its computer network to see who ran it. “You have a hole in your software,” he recalls telling Greg Kidd, the company’s chairman. Kidd wanted to hire him, and asked Dorsey if it would be O.K. for him to leave school. “I was worried about his mother,” Kidd remembers. Dorsey replied that the school would be O.K.—meaning that the computing class where he was a teaching assistant could get along without him. “It was the first of many miscommunications I had with Jack,” Kidd told me, laughing.

Dorsey left college and moved to New York. Kidd offered to let him live in one of two properties that the company leased: a house in Great Neck or an apartment, on John Street in Manhattan, that overlooked an airshaft. Dorsey preferred the latter: “I got to take a subway every morning to work!” Kidd paid him six hundred dollars a week, and Dorsey spent his earnings at such clubs as C.B.G.B. and Coney Island High. That fall, he also enrolled at N.Y.U.—a concession to “parental pressure.”

Kidd’s company attempted to democratize bike-messenger work by allowing any deliverer to bid for a job. Dorsey developed software to run the new system. He and Kidd became close, although Kidd says, “I don’t know what it means to hang out with Jack Dorsey. He doesn’t talk a lot—he listens and he’s thoughtful.”

This was the era of rampant Web startups. Dorsey and Kidd pushed for a larger presence on the Internet, and wound up leaving the company in frustration. At the end of 1999, they moved to San Francisco and started a Web-based dispatch firm. (Dorsey withdrew from N.Y.U. a semester short of graduating.) Dorsey took on the look of a bike messenger, with dyed dreadlocks that ranged from bright blue to peroxide orange. Things did not go well at the new company. Its emphasis on honing technology ran counter to the board’s push for sales, and soon Dorsey was fired. The company failed during the dot-com bust.

Dorsey moved, in short order, to Richmond, Virginia, and Cambridge, Massachusetts, to be with women he was dating. Neither relationship worked out. Parsing past failures does not come easily to him. He says of his tendency to keep to himself, “I think it can be, in the worst case, isolating to girlfriends and friends.” He adds, “Mainly, the relationships ended more just from the feeling that this isn’t really meant to be. I’m sure the independence thing and being in my head added up, though.”

In 2002, at the age of twenty-six, Dorsey went home. “I felt like a failure,” he says. “Here I was, back in St. Louis.” He coded for his father, who had started his own mass-spectrometer business, and he studied botanical illustration. He enjoyed visiting the Missouri Botanical Garden, where he did drawing studies of a banyan tree, with its forking roots. Dorsey remembers that his wrists ached “from years of programming.” He tried using keyboards with layouts that minimized finger movement, but they didn’t help much. Faced with the need for massage therapy, he decided to enter the field. “When something interests me, I don’t just read about it,” he says. “I do it. I go all in.” He hoped to open a chair-massage service for programmers, in San Francisco. He imagined having a place that “gave programmers code therapy and massage therapy.” (He promises that he was serious.) But when he went back to San Francisco, in 2005, he discovered that “everyone was a massage therapist,” and dropped the idea.

Around this time, Dorsey got a tattoo on his left forearm of an elongated “S,” which represented three things that interested him: an f-hole on a violin; a collarbone, which he considers the most beautiful bone in the body; and the integral symbol from calculus. He also got a nose ring. “That really hurt,” he says. “That was a mistake.”

Not wanting to return to the grind of daily programming, he agreed to look after Kidd’s young daughter in exchange for room and board. He moved into a shed behind Kidd’s house, on the Berkeley-Oakland border. Babysitting was an unlikely job for an introverted man in his twenties, but he excelled at it. “He had that ability to be very present, and really small kids know whether you’re present,” Kidd says. At night, Dorsey began experimenting again with coding, rediscovering “the purity of making cool little things.” He searched ads on Craigslist and found an opportunity: the ticketing program for the tourist ferry to Alcatraz needed a revision. The system was beset by fraud, and Dorsey wrote a more secure program.

After the ferry job, Dorsey cast around for new opportunities. He studied figure drawing after reading that Scott Morrison, a jeanmaker he admired, preferred designers who had such training. “He approached denim like it was a living journal,” Dorsey says. Later, he took classes in fashion design at Apparel Arts, in the Dogpatch neighborhood of San Francisco. He designed a pencil skirt and an asymmetrical one. He put them in a closet and, eventually, threw them out.

One day in 2005, when Dorsey was at a café in the South Park neighborhood of San Francisco, he saw Evan Williams, a well-known Internet entrepreneur, who, two years earlier, had sold Blogger to Google. Williams, then thirty-three, had helped launch a company called Odeo, which allowed users to create and share podcasts. “I could care less about podcasting, but I liked his style,” Dorsey remembers. “He had an eye for good Web design. And he came from the Midwest—a farm boy from Nebraska.” Dorsey sent Odeo his résumé, which listed his name only as “Jack.” Williams wasn’t overly impressed, but he needed a coder, so he hired Dorsey. Dom Sagolla, another engineer at Odeo, says, “He was a grunt, like me. He wasn’t even a lead developer. He was a line-level engineer.” For the next month, Dorsey tried, in vain, to appear interested in podcasting. When Apple announced a version of iTunes with a podcast store, Odeo looked doomed.

Searching for a new direction for the company, Williams declared a series of “hackathons.” The programmers could work on anything they wanted, in the hope that Odeo might find a new direction. Dorsey had never stopped thinking about the mapping program he had written—the one with people missing from it. At various times, he had explored ways of importing people into his schematic cyberworld. While looking after Greg Kidd’s daughter, he had designed a program that told users of Google who else was searching for the same thing and allowed them to communicate with one another. Kidd was fascinated by the idea. “It suggested you could use Google not just to find information but to find people,” he says. Dorsey created another application, postcard x, which automatically offered a user the name and address of a stranger who wanted to receive a postcard. “About ten thousand people did it,” Dorsey recalls. He wrote a program allowing a user to write a note that disappeared once the recipient read it. “I loved the impermanence of that,” he says.

Over the years, AOL’s Instant Messenger program had also caught his eye, particularly the “Away” tags that indicated when users were unavailable to chat. The tags provided just the sort of information that Dorsey liked to have about people: where they were and what they were doing. In 2000, he began using a mobile device called the RIM 850, an early version of the BlackBerry. It could access e-mail—then a novel capability—and Dorsey started designing programs for the system. One day, on a pad of lined paper, he wrote down two examples of a short message that a user could share with a list of contacts: “in bed” and “going to park.” He then jotted down a prompt: “know someone?” He was imagining the kind of search mechanism that later became central to social media. He wrote some code, and named the result STAT.US. Dorsey took his phone to Golden Gate Park and informed his friends, “I’m at the bison paddock.” The results were disappointing. As he recalls it, “No one had a BlackBerry, and no one cared.”

By 2006, however, computing had begun moving beyond computers, and users increasingly expected not just to search for information but to contribute it. “It was the beginning of the participatory Internet,” Biz Stone, who was then working at Odeo, remembers. MySpace was flourishing, as was LiveJournal, for which Dorsey had done some contract work. At Odeo, a colleague introduced Dorsey to S.M.S., the texting protocol. “I fell in love with the technology,” Dorsey remembers. “It was rough around the edges, cheap, and it was on every single device out there.” Texting had never been particularly popular in the United States, but that was rapidly changing. He and others at the company began discussing the technology’s potential.

During a hackathon, Dorsey took a walk with Sagolla, who ran Odeo’s quality-assurance program, and Florian Weber, a German programmer. In a story that Dorsey has told many times, the three were sitting on a slide in a South Park playground when he suggested, “What if we used S.M.S. to report what you’re doing, and also to receive news of what everyone else is doing?” He told me, “I wasn’t considering what everyone else wanted. I was considering what I wanted.” Sagolla wondered what such a notification system could do that audio messages couldn’t. “What if you’re in a loud night club?” Dorsey asked. They decided that Sagolla, who was a better public speaker, would propose the project to Williams and their colleagues at Odeo.

Sagolla made a brief presentation, pointing out how useful the program could be in various social contexts, including in an emergency. Others at the company had already proposed projects involving S.M.S.—among them Off Da Chainz, which helped users organize events—and not everyone immediately understood why this new idea was any better. At some point, Dorsey considered leaving, but Noah Glass, who had founded Odeo with Williams, put his weight behind the project. Glass was a key supporter: Sagolla remembers him as “handsome, well spoken, erudite, witty, and loud.” Under Glass’s supervision, Dorsey and Weber wrote the code in two weeks.

Once there was a prototype, everyone at Odeo came to see the service’s potential. Because cell phones often make a buzzing, jumpy noise upon receiving text messages, the team considered calling the service Jitter or Twitch. One day, Glass pulled out the dictionary and suggested Twitter instead. Everyone liked the name, but it had already been taken by a bird Web site. Williams bought the site for seventy-five hundred dollars, but the service launched under the name twttr. It looked cool, the odd spelling evoking the hot photo-sharing service Flickr. The limit for an S.M.S. message was a hundred and sixty characters; because users of the new network would identify themselves by appending their name to each message, the company limited posts to a hundred and forty characters.

The development of Twitter was a collaborative process, and each contributor had a slightly different template in mind. Evan Henshaw-Plath, an engineer known within the company as Rabble, told me that he and another Odeo programmer, Blaine Cook, were anarchists who wanted the new service to “work like TXTMob”—software that they had designed to assist liberal protesters at the 2004 Republican Convention. Henshaw-Plath added that Williams “wanted it to work like Blogger, Jack wanted the dispatch stuff, and Noah was passionate about the way we communicate.” Among the players, there is general agreement that Dorsey played a crucial role. Weber told me, “When it comes to driving the vision and pushing it through, that’s absolutely Jack.” Two years ago, George Zachary, who was an investor in both Odeo and Twitter, told Business Insider that, although Glass was “a huge advocate” for Twitter, Dorsey was “the real core founder.”

Over the years, there has been much jockeying and positioning among the creators. For a time, the founding myth seemed to encompass only Williams and Stone, with Dorsey the forgotten Beatle. But Dorsey sedulously worked his way back into public view. In 2011, around the fifth anniversary of Twitter, he tweeted a link to an old Flickr post that contained a photograph of the notepad with the “in bed” and “going to park” scrawls. Around this time, Glass, who had dropped out of the tech world, complained to Business Insider that his contributions had been airbrushed out of Twitter’s official picture. His reappearance prompted Williams to tweet an acknowledgment that Glass “never got enough credit for his early role at Twitter.” The tweet stopped short of an apology.

Glass recently expanded on his disappointment to Nick Bilton, a Times reporter who has written a book about Twitter. Glass recalls listening to Dorsey’s vision of an S.M.S. status updater after a long night of partying together. Bilton writes that, as they sat in a car, sobering up, Glass—who was in the midst of a fractious divorce—looked out the window, “thinking about his failing marriage and how alone he felt.” This feeling of isolation suddenly led to an “epiphany”: the key to Twitter was its conversationality. In this telling, Glass plays McCoy to Dorsey’s Spock, transforming a geeky idea into a social one. Not long afterward, Glass turned to his blog and declared, nebulously, that “the cold concept of status” had become “imbued with the radiant hues of human emotion, need and desire.”

Glass has now put forth a foundation myth of his own, but other Odeo veterans are skeptical of its significance. Florian Weber, the coder, told me, “Noah never said Twitter should be about conversations! And the way Noah used Twitter itself was in the old form of updates—‘I’m having dinner with blah-blah-blah,’ that sort of stuff.” (July 31, 2006: “at bestbuy … buying.”) Zachary, the investor, says, “What Twitter is now—I never heard Noah talk about that.” Dorsey, for his part, remembers the car conversation as a long one in which Glass “finally got” what he and Weber “were trying to do”; as Dorsey sees it, Glass needed to focus on the emotional implications of the idea in order to appreciate it. In any case, Glass’s putative breakthrough didn’t inform the design of Twitter. Conversation was not seamlessly integrated into the service until November, 2006, when a user, Robert Andersen, used the @ symbol to indicate that he was directing a tweet at a specific user. Dorsey says, “If you look at all the early tweets, there are no conversations until people started using the @ symbol. Even Noah wasn’t using it to comment to other people.”

One reason that the origin story of Twitter has proved so complicated is that the service itself is so bare-bones. At one Odeo presentation, Dorsey defined Twitter, crisply, as an “R.S.S. for S.M.S.” Over time, this basic function was modified by users, much in the way that police officials established specific protocols for exchanging information over the radio. A poster on the Y Combinator blog once commented, perceptively, that Twitter was “more of a discovery than an invention.”

In March, 2006, the service’s first official message went out, from Dorsey’s account: “just setting up my twttr.” Twelve minutes later, Dorsey sent another one: “inviting coworkers.” The messages were in lowercase, he says, because he “was into e.e. cummings.” Dorsey’s words have since been retweeted seventeen thousand times.

Twitter was taking off, and personalities were chafing. Glass asked Williams if he could run the project as a stand-alone entity; Williams said no. Glass, according to the others, grew disruptively erratic, his personal life compounding the stress of working in a startup. Sagolla told me that Glass’s behavior was “unpredictable,” and remembers him screaming at him over a proposed logo: “ ‘No birds. No more fucking birds!’ He yelled at me like I was an idiot.” Zachary recalls Glass “going from elated to being despondent pretty quickly.”

Eventually, the decision was made to fire Glass. Bilton reports that Dorsey threatened to quit unless Glass was forced out. Dorsey says otherwise: “I didn’t give an ultimatum. . . . I didn’t have that leverage. Ev made his decision.” As Dorsey recalls it, “Ev asked me, ‘Should we let Noah go?’ And I said, ‘I don’t think I can work with him in his current state.’ ” Zachary recalls Williams announcing that he was going to fire Glass, because “no one wanted to deal with him.”

By mid-August, 2006, Glass had left the company. Later, Williams gave him some stock in Twitter. To this day, Glass’s Twitter bio reads, “I started this.”

Twitter benefitted enormously from good timing. In 2006, Facebook added the “status update” to its service, priming people to document their lives in short bursts. More cell phones were getting connected to the Internet, and the iPhone soon put millions of Web browsers into people’s hands, allowing them to tweet without incurring text-messaging charges.

Despite Glass’s protests, Twitter’s home page featured a cute white bird, which has become iconic, and a question: “What are you doing?” Twitter began with a “friend” function, in an apparent echo of Facebook, but this was dropped in favor of a simpler format in which users could simply “follow” others, including strangers. Dorsey said, “The way we saw it is that you write on the wall and they choose to follow what you’re doing for a while, and they can always leave.”

By the fall of 2006, Twitter had amassed fewer than five thousand registered users. In March, 2007, at the South by Southwest festival—an annual event, in Austin, that promotes new music and software—Twitter named half a dozen attendees who were enthusiastic tweeters its “ambassadors,” and posted their messages, in large type, on plasma screens in the lobby of the conference center. These people, Dorsey remembers, “were really good at Twitter and really popular folks.” Attendees who signed up for Twitter at the conference got their tweets added to the screens. The stunt—insiders showing off for other insiders—was an instant hit. One message read, “Watching myself on twitter feed.” Dodgeball, a rival location-based service, was soon deemed inferior. (It shut down in 2009.) Gawker pronounced Twitter “aflame” and added that the company could “make a Facebook-sized blowup among the general public.”

Dorsey’s urge to keep track of what other people were doing had become a communications revolution. “One could change the world with one hundred and forty characters,” he tweeted, a month before South by Southwest. It was a grandiose proclamation, but one of the surprising things about Twitter was that so many worthwhile things could be said so tersely. Maybe they were even better said that way. Enforced brevity was the ultimate editor.

One reason that Twitter did not go the way of Dodgeball is that its very basic interface lent itself to all sorts of purposes, many of them unforeseen by its designers. Neither Dorsey nor the other founders created retweeting or hashtags, let alone the @-reply. They did not expect so many celebrities to start feeds. (On Twitter, anyone can follow you, but it’s done at a safe distance—you have to consent to receive a private message before someone can send you one.) Twitter turned out to be an ideal medium for celebrities trying to create a simulacrum of intimacy with fans. The top three Twitter accounts belong to pop stars; Justin Bieber is in the lead, with 45.6 million followers, just ahead of Katy Perry and Lady Gaga. (Obama’s account, the highest-ranked outside the entertainment industry, has just under thirty-eight million.)

Tiny messages, published in real time, have a particular power in countries where computers are scarce and Internet connections spotty. During the 2009 student protests in Iran against President Mahmoud Ahmadinejad, the State Department deemed Twitter so important that it asked the service to delay shutting down for routine maintenance. Twitter was crucial during the Arab Spring. (Blaine Cook, the Odeo programmer who had seen parallels between Twitter and TXTMob, remembers telling himself, “Yeah, it worked!”)

Dorsey told me, “I believe fundamentally that the next Gloria Steinem, the next Gandhi, the next Martin Luther King—they’re out there and they’re actually using Twitter today. And our job is to insure that people find them.”

In 2009, Twitter changed its home-page greeting from “What are you doing?” to “What’s happening?” This shift, which Evan Williams has said that he instigated, was part of an effort to push Twitter in a more topical, serious direction. But pushing Twitter in any direction is an impossible task, because each user winnows the data stream in a radically different way. One subscriber can create a virtual tabloid by following only gossips; another can construct a bespoke community of particle physicists and hot-yoga obsessives. The best tweeters don’t sound anything alike. Joyce Carol Oates’s struggles for profundity in the face of the format have a sharp poignancy: “Original purpose of religion—(unconscious) wish to live forever. Invent God, but then a priest-caste sees an opportunity & takes over. No?” The comedian Rob Delaney filthily mocks the clichés of the form: “RT if you’re being fingered in a Quizno’s.”

Even though the family police scanner helped inspire Twitter, Dorsey says that he didn’t fully appreciate its potential to become a news source until January, 2009, when Janis Krums, a passenger on a ferry crossing the Hudson River, tweeted a photograph of a U.S. Airways Airbus A320 that had just crash-landed in the water, after running into a flock of geese. The snapshot, showing dozens of people standing on the wings of the doomed aircraft, became the defining image of the event. But the words that Krums chose to accompany the photograph captured even better Twitter’s singular mixture of the monumental and the mundane: “There’s a plane in the Hudson. I’m on the ferry going to pick up the people. Crazy.”

After South by Southwest, Twitter achieved the hockey-stick growth curve that is coveted in Silicon Valley. By 2008, the service had 1.3 million users; by 2010, it had more than a hundred million, and eighty-seven per cent of Americans knew what Twitter was.

This was an impressive achievement, but Twitter always seemed too easy to people, too insubstantial. It didn’t help that Biz Stone, one of the founders, was an avowed master of the dopey tweet: “Wow, Amtrak serves a vegan burger! Nice.” Perhaps it was the simplicity of the idea that rankled, or its exploitation by celebrities. To some in Silicon Valley, Twitter’s growth curve most resembled that of a fad, confirming that the endeavor was somehow gimcrack, and that Dorsey, by extension, was not quite top-level. The number of users grew so fast that the small team behind the project could not keep up. In Williams’s words, it was “a six-foot-tall sixth grader.” The service crashed frequently, prompting the display of the notorious “fail whale”—a flock of Twitter birds lifting up a cheery cetacean, accompanied by an apology. “We weren’t changing the world when we were doing this thing,” Stone recalls. “We were in an office that had rats in the basement, our team was fighting with each other, and everyone thought it was stupid.” Dorsey remembers the two anarchist programmers refusing to sit during sit-down meetings and refusing to stand during the standup ones.

Meanwhile, a deeper confusion played out among the founders. “For a long time, the world didn’t know what Twitter was, and neither did we, exactly,” one of them told me. Should it be an open platform that anyone could program for and profit from? Or should it be a closed system, like Facebook, with a clear financial plan? Well into 2009, it wasn’t evident how Twitter could start earning money. To service its vast base of users, the company had to go back to investors repeatedly for money, ultimately requiring seven hundred million dollars.

In 2007, Williams had named Dorsey the company’s first C.E.O., calling him “the genius behind the Twitter idea.” According to an insider, Dorsey was given twenty per cent of the company. But the enthusiasm and the independence that had led Dorsey thus far did not translate well into management. “There were a lot of things we could have done better,” Dorsey acknowledges. “The system was going down a lot. We didn’t have any instrumentation”—that is, they had little ability to gauge when the capacity of the system was being tested. “A lot of that was because we were coming out of another company.” This explanation edits out his own failings: the thirty or so employees Twitter had at the time were irritated by his management style, especially by his tendency to leave work early for things like yoga classes. (Dorsey says that he always resumed working later in the evening.) For a while, Dorsey had a C.E.O. coach, but his taste for life as a shaggy polymath kept bumping into his responsibility as the head of a company. The press wondered how Twitter would generate revenue. Dorsey points out that startups often take years to begin making money, and that nobody at Twitter expected it to be quick at turning a profit. Nevertheless, after the financial crisis of September, 2008, Twitter’s board—at the urging of Williams, the company’s top shareholder—forced Dorsey out and replaced him with Williams. Dorsey retained the title of chairman, but it was purely ceremonial.

He was deeply hurt. He says of Williams, “He didn’t want to be C.E.O., and then he did.” Williams insists that he prefers starting companies to running them, and that he took action only because Dorsey was in over his head. In his view, Dorsey simply wasn’t ready to be a C.E.O. Neither was Williams, it turned out—in 2011, he was removed by Twitter’s board. Williams’s allies believe that Dorsey engineered his ouster. Biz Stone says, “They think he worked on the board for two years, like the Count of Monte Cristo, to get his revenge.” Dorsey insists that he was not the cause. When he left the C.E.O. job, he ceded his voting rights to Williams. “I didn’t have that much control,” Dorsey says. “He was the largest shareholder.” But Dorsey acknowledges that he may have been working to turn the tables. “I was chairman,” he says. “Many people were coming to me. I would say, ‘You should bring that up with the board, not just to me.’ ” He adds, “Was I thinking, Screw Ev? Emotionally, was I asking that? I don’t know. Maybe.” After Dick Costolo, a Twitter executive, was promoted to C.E.O., Dorsey resumed an active role at the company.

Dorsey says that the infighting never diminished his joy in having created something he loved. He still gets giddy when he remembers the first days of his Twitter account: “We’d all go off, and . . . I’d get a text. My phone vibrates and, like, Ev is in Napa. And Biz is, like, working on his house, pulling up carpet. And Jeremy is experiencing an earthquake in Oakland—like, all at the same time, right? It’s so cool.”

Dorsey’s mother loved Twitter, too: “He’s not the kind of guy who calls every day. With Twitter, we could see what he was doing.”

After Dorsey lost his position as C.E.O., he felt that he had something to prove. He looked like a one-hit wonder, the handsome front man—the Seinfeld of the “Seinfeld” of the Internet. As some Silicon Valley skeptics saw it, Dorsey had lucked into one good idea, programmed some simple code, bumbled along as the company surged to success, then claimed more credit than was his due. Dorsey says that he faced a lot of condescension: “People would say to me, ‘It’s just a tool so people can update about what they had for breakfast.’ ”

Dorsey had just traded in the four-hundred-and-fifty-square-foot apartment he had rented near the office for a thirteen-hundred-square-foot loft, in the same building. He dated a dancer in the San Francisco Ballet. He considered joining a venture-capital firm, but decided against it.

He needed another tangible problem to solve. It had to be something that affected him personally—he’d learned this from toiling on podcasts. “I’m somewhat selfish in that regard,” he says. “I want to use these things in the world, and you make the bet that other people want to use them.” He played around with various social-media tools. (“I can’t tell you about them, because I might want to do them one day!” he says.) The right challenge came his way a few months later, when a longtime friend, an artist and tech entrepreneur named Jim McKelvey, complained that he’d failed to sell a piece of glasswork to an overseas buyer. The woman had been willing to pay two thousand dollars for it, but McKelvey wasn’t able to accept her credit card. Dorsey and McKelvey felt that they’d detected a glitch in a fundamental system. They studied the way payments were processed, and concluded that it was muddled, unnecessarily expensive, and ugly, with hulking cash registers, mounds of paper receipts, hidden charges, and insulting credit checks for merchants. The system lacked wabi-sabi. Greg Kidd remembers talking to Dorsey about the possible project: “He said one of those Jack things. ‘You know, Greg, payments are very intimate.’ That’s all he said.”

Dorsey began to think of payments not as money but as “commerce, which is conversation.” But chat on the Internet is wide-open territory; commercial transactions are regulated by banks and populated by tough players. Dorsey, having spent much of his youth in debt, “hated the credit-card companies.” He told me, “It actually gave me a lot of pause. Do I really want to support more of this instrument that leads a lot of people to bad financial health?” Yet he saw another chance to democratize a field, and to design something sturdy and elegant.

He and McKelvey set out to make a portable credit-card reader that anyone could use to accept a payment. Dorsey focussed on the software, McKelvey on the hardware. They assembled a small team, paying for them, in part, by selling some of Dorsey’s shares in Twitter. He and McKelvey hoped to break some rules. The opportunity arrived in February, 2009, when they realized that they could attach a credit-card reader to an iPhone by appropriating the audio jack. They could piggyback on the computing power of the phone and sidestep Apple’s patented dock connector. “It was faster, more reliable, and royalty-free,” McKelvey recalls. In May, 2009, Dorsey tweeted, “Getting ready to embark on something new and entirely different. Excited!”

The team soon had a prototype. Dorsey invited Sagolla, his coder friend, to meet him at Blue Bottle. After grilling Sagolla about his spending habits, Dorsey asked to look at his credit card. Dorsey attached the prototype to his iPhone, swiped the card, and announced that Sagolla had just bought him breakfast. (Shortly afterward, while in New York, he pulled the same trick on Mayor Michael Bloomberg, who demanded the money back.)

The service had to compete with other Internet payment companies, but the biggest such firm, PayPal, had a lacklustre interface, and seemed an easy target. Dorsey knew that choosing a good name was key. First, he and his team called the service Squirrel, with its suggestion of small-bore savings, and made the credit-card reader in the shape of an acorn. “A cute idea, but probably not a great one,” Dorsey says. The device was renamed Square, and reshaped accordingly.

Dorsey says that he did not find Square easy to sell to venture capitalists. The country was in a deep recession, and Square was not the sort of thing investors expected from a social-media guy. It was also a risk to put himself forward as a C.E.O., rather than just as a founder. “People weren’t really sure why I left Twitter in the first place,” he says. “And they saw me as having created something that was simultaneously big but also, possibly, trivial.” To counter resistance, Dorsey made a presentation slide titled “140 Reasons Square Will Fail.”

The project began to attract funding—Evan Williams connected Dorsey to his first equity investor. Dorsey says that he liked the difficulty of the effort. It satisfies him the way romance does. “I thrive on tension,” he says, sounding as if he were preparing his next creation myth. “If I had a relationship where nothing was ever wrong and we were never debating or arguing, I don’t think we would ever grow. There’s no change.” He observes, “We created Twitter in a depression, or funk, in the Odeo office, and Square in the heat of a financial crisis. It allows you to be creative, a depressive moment.”

To reinvent the payment industry, Dorsey avoided hiring employees who came from it. “Of the six hundred people here, only ten ever worked in finance,” he told me. Square’s focus, which he traces to his mother’s coffee shop, is on the smaller merchant who used to find accepting credit cards too expensive or too cumbersome. In St. Louis, Dorsey recently held a town-hall meeting for small businesses. The line outside was long. He had selected four merchants to appear onstage with him: a bike-shop owner, an artisanal jeweller, a vegan baker, and a coffeehouse proprietor. Dorsey sees no contradiction between these merchants and Starbucks, which is Square’s largest customer and a major investor. Companies like Visa and MasterCard have a dizzying number of rates for swipe fees. Dorsey wants to level the playing field by having Square merchants pay the same transaction fee: 2.75 per cent per swipe.

The company is now rolling out SquareCash, which will allow users to send and receive money by e-mail—a service that many companies have offered, but none with great success. After just three years, Square now processes fifteen billion dollars a year, not including Starbucks. The company has been valued at $3.25 billion. (According to a recent filing, Dorsey owns about a third of it, McKelvey about ten per cent.) Although continued success is not certain—it is a crowded field—Dorsey has impressed his peers. Williams told me that he wishes he’d invested in Square, saying, “What I have seen in the last few years as a Jack observer is his intense focus on his work and on himself to become better. It’s amazing.”

Mark Zuckerberg, the Facebook founder, also admires Dorsey’s company: “The hardest thing as a founder is to keep your . . . vision as a company grows. Jack has been clear and disciplined.” For a time, Zuckerberg and Dorsey met regularly for dinner. When they got together, Zuckerberg cooked. During the meal, they warily conversed about technological trends. Dorsey says, “He’d ask me if I had any ideas. Am I seeing anything in video? And, immediately, I’d turn back the question: ‘What are you guys seeing?’ ”

Dorsey supervised the design of Square’s new headquarters, which occupy the largest rental floor in San Francisco. His taste reflects Silicon Valley’s sometimes silly literalism. The conference rooms are named for streets in San Francisco. Other rooms are named for currencies: the yuan, the kroner. Copies of a book on wabi-sabi sit on a lending shelf, along with Sheryl Sandberg’s “Lean In.” (Dorsey is active in a group named Girls Who Code.) On Fridays, the employees, led by Dorsey, devote themselves to volunteer work. Square’s credit-card reader has a simple beauty, and product managers are called editors. To inculcate his love of the aesthetic, Dorsey has led his staff on outings to the Golden Gate Bridge and to an art exhibit on Man Ray and Lee Miller, at the California Palace of the Legion of Honor.

No one questions Dorsey’s right to be C.E.O. this time, perhaps because this time he built his own team. And he has scaled himself up with surprising ease: he now consorts with many of the nation’s top business leaders. (A friend describes the process as “Jack doing A/B tests on his personality.”) His old friend Biz Stone recalls a recent conversation: “He’s, like, ‘Hey you should meet my friend.’ ‘Who’s your friend’? ‘Oh, my friend is, like, whatever, the guy who owns Time Warner.’ ‘Oh, that’s your friend. Interesting.’ ” Teasing aside, Stone is impressed by the transition he has seen, by what he calls Dorsey’s new ability to “sort of embody his own persona in a graceful and leadership-y kind of way. It’s very rare for a programmer—I mean, a geeky programmer kid—to, in a relatively quick amount of time, become a global leader. . . . Larry Page is the C.E.O. of Google, but he doesn’t have anywhere the qualities that Jack has.”

His plans do not lack ambition. For some time now, Dorsey has been saying that he would like one day to be the mayor of New York. It’s a curious goal for someone who has lived in California for eight years, who has no experience in public life, and for whom human contact is a challenge—it’s one thing to look after a friend’s child, another to kiss a stranger’s baby. He does a creditable job on television, but never seems fully comfortable. Two years ago, Dorsey interviewed President Obama, in the White House, for an event called the Twitter Town Hall; the Los Angeles Times described Dorsey as a “stiff, sweaty, and serious emcee.”

Last month, at a Square recruiting session at Columbia University, the first question the engineering students asked Dorsey was about the mayoralty. He assured them that no such move was imminent; he could make more of a difference for now in the software world. He praised Bloomberg’s ability to master and improve the various systems of the city. There was no mention of his effect on individual lives. To Dorsey, the city was an engineering problem: Bloomberg had improved the interface and, thus, the experience of being a New Yorker. The audience nodded, though. Dorsey spoke their language. He told me that being mayor would come with “a lot of constraints, but I do well with constraints.”

Certainly, if Square eventually follows Twitter and becomes a public company, Dorsey would have extraordinary resources to fund a campaign. He owns 23.4 million shares of Twitter stock; an initial public offering is upcoming, and his stake could be worth nearly half a billion dollars. In March, at a celebration of Twitter’s seventh anniversary, Dorsey asked Bloomberg if he had any suggestions for how to succeed him in his job. Stone recalls, “Bloomberg told him, ‘Become a billionaire!’ I was joking with him recently, and I said, ‘Well, you’ve checked that box off.’ ”

Of course, Dorsey would have to run not just on his money but on his résumé. He may admire data-driven competence, but he has not yet demonstrated Bloomberg’s gift for it. If Dorsey truly wants to be taken seriously, he will have to extend his success at Square. Fostering sustained growth at a payment company, however, may not satisfy the aesthete in him. Another reboot seems possible for the former slacker who loved sketching plants at the Missouri Botanical Garden. Recently, while telling me that he was convinced that Square had achieved only “one per cent” of its potential, he paused. “I’m at a point in my life when I want to go deeper,” he said. “I could just move down to Marfa and become an artist.” ♦